Mathematics for the interested outsider

Approximating Sets of Finite Measure

So, we’ve got a -finite measure on a ring , and we extend it to a measure on the -ring . But often it’s a lot more convenient to work with itself than the whole of . So, to what extent can we do this efficiently?

As it turns out, if has finite measure and , then we can find a set so that .

About this weblog

This is mainly an expository blath, with occasional high-level excursions, humorous observations, rants, and musings. The main-line exposition should be accessible to the “Generally Interested Lay Audience”, as long as you trace the links back towards the basics. Check the sidebar for specific topics (under “Categories”).

I’m in the process of tweaking some aspects of the site to make it easier to refer back to older topics, so try to make the best of it for now.